I have never done it, but if I had to, I would put Oxyclean and hot water in an empty mayonnaise jar, then set the jar on the top step of a ladder and put the pull strings in the jar and let them soak for an hour or so. Then I would rinse them the same way - clean water in a jar.

Great advice, but if your ropes are dirty, your blinds are probably too. You may want to take them down and put them in the tub with the oxy cleaner. If there's grease on them, use an oxy/enzyme cleaner. That's how I do it.

They might also be yellow from the sun. UV sun damage might not come out with any cleaner. I had some in an rv that I couldn't whiten after that.

If you need new blinds, go to jcpenney.com because it's the lowest price on blinds I've ever seen!
My husband is a contractor and builds homes. We have to buy window coverings that are nice (because they're pricey homes) but don't soak up all our budget.